Order = 138297600 = 28.32.52.74.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of S4(7) are a, b where a is in class 2A, b has order 5 and ab has order 7.
Standard generators of 2.S4(7) = Sp4(7) are preimages A, B where B has order 5 and AB has order 7.
Standard generators of S4(7):2 are c, d where c is in class 2C, d has order 5 and cd has order 12.
Standard generators of 2.S4(7):2 are preimages C, D where D has order 5.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| S4(7) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of S4(7)
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- Permutation representations:
Number of points ID Generators Description Link 400 a Std Details 400 b Std Details 1176 Std Details 1225 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[b7] 25 a Std Details 0 C 25 b Std Details 0 Z 126 Std Details 0 Z 175 a Std Details 0 Z 175 b Std Details 0 Z 224 Std Details 7 GF(7) 5 Std Details
Representations of 2.S4(7)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 7 GF(7) 4 Std Details
Representations of S4(7):2
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- Permutation representations:
Number of points ID Generators Description Link 400 a Std Details 400 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 7 GF(7) 5 Std Details
Representations of 2.S4(7):2
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 7 GF(7) 4 Std Details